Talk:Affine symmetric group/GA1

1455:, paying very careful attention to exactly what it says about sourcing? Note in particular that it is much less strict than the DYK sourcing rules, which themselves require only a single footnote per paragraph. The relevant rules for GA are 2b, which does not say anything about what should be referenced, only that when things are referenced their sources should be reliable, and 2c, which says in its entirety "it contains no original research". Not that all content is actually sourced to anything, but merely that it is known material rather than something entirely made up as new material for the Knowledge article. On what basis of GA rules are you making these bizarre demands that material that merely explains the structure of the article itself must somehow have a footnote and that this footnote requirement would be satisfied by putting something inane and non-referency into the footnote? In what way do any of these statements constitute original research? Wouldn't putting an inane non-citation into a reference violate 2b, which requires that the references be reliable sources? How do you read the rules as in any way causing such a requirement to exist? What words of the rules are you following in this? — 1377:

is an argument that they should be removed (without any changes to the text). Both remaining cn tags concern the following situation: there are multiple valid conventions in the literature about how to present, display, or denote something; while each is separately valid, the conventions are incompatible with each other, and so any given expositor is forced to choose one of them. (For example, one could choose to number the rows of a matrix so that the indices increase from top to bottom, or one could choose to number them so that they increase from bottom to top.) Both sentences that are tagged explain to the reader what convention is being used in this article. This is essential information (otherwise it leaves ambiguity as to which of several incompatible choices has been made), but it is impossible in principle to cite it (because they are statements about this article itself). I suppose for the first one I could remove the figure (thereby removing the need to explain what convention is being used in the figure), but the second one seems completely unavoidable to me. Any thoughts or comments you had are welcome. --

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varies between the two modes of stating things without the context of where it came from ("the affine symmetric group is ...") versus attributing particular ideas to particular people ("Shi showed that ..."). I'm not sure I can exactly justify each choice about which fact gets introduced which way, but roughly I think the division is between "folklore" and "things everyone knows" (esp. in the context where you might write a background section of a paper and begin, "for more information on these topics, see " somewhere at the beginning) on one hand, and things that are more recent, have only appeared in the original research papers (rather than being re-exposited elsewhere), etc. One might hope that mentioning particular authors also gives a sense of the dynamic of the field (something that you have noted was not otherwise conveyed well -- though now with a history section it's a bit better).

519:. Much of your review is helpful, but I wanted to comment on this part. I do not agree with the view that the Harvard references here are deprecated since they are not references in the Knowledge sense, but are used to refer to specific works. Writing "Smith wrote in 1999" and "In (Smith 1999)" are essentially the same and don't appear (to me) to be the deprecated style, since it is merely a way of writing names, not a way of citing sources for specific information. Now, this does raise an interesting question - should the "Representation theory and an affine Robinson–Schensted correspondence" section have references, or is the textual clue that they refer to specific works enough? Dunno, but something to think about. Also, even if it were a citation style, consistency in citation styles is not required by the GA criteria. (Deprecation is a separate issue.) 225:. The first two are summary sentences of the subsections that follow them -- they are not meant to be free-standing factual claims, but rather navigational aids that briefly give the reader an overview of what is coming. I would have thought that they did not need independent citations (for the same reason that the introductory section of articles does not). (I mean, I suppose that I could copy some lower-occuring citations up to these sentences, if you thought that would be better.) The third example is a sentence about navigating the article -- it tells the reader that we have introduced X and we have introduced Y and where in the article to find the relationship between them. It has no factual content to cite. May I remove it? Or, is there some way I can reword that you think might avoid confusion here? Thanks again, 483:, or stand-ins for the papers being referred to, rather than at the ends of sentences as sources only visible on mouseover as we typically do, regardless of the citation style being used. This, again, recalls a common issue in GANs for me, in which it is often possible to detect the involvement of different writers at different times due to subtle and not-so-subtle changes in focus and style, often in citations ... in other words, the nominator didn't go through the whole article after expanding it to make sure the voice was consistent. But, again, that is clearly not the issue here, since the article's voice is the same throughout. 1745:, which merely stated which of multiple notational conventions the article was following, and refusing to back down from that demand after multiple editors tried to intervene. However, Case's responses to why he was refusing to back down did not make me confident in the depth of the rest of the review: as far as I can tell it amounted to checking sourcing by whether there were lots of little blue numbered footnote markers and not by whether the material needed sources and whether the sources were adequate for the material. — 421:: a brief history section explaining how the concept came to be discovered or something like that. This article IMO could use one. As it is it just seems as if the idea of affine symmetric groups just appeared on a stone tablet lowered from a flying saucer by a beam of light. Surely this is not the case ... a reader would get a better handle on the subject understanding where it came from, who (if they are notable) developed and perhaps named the concept, when, and where. And maybe they won an award for doing this. 1572:, I think your comment has convinced me first that the description of the image should really be in the image caption, not in the text. (The reason to display the matrix this way is that if you don't, it's very hard to see the isolated 1s in a huge sea of 0s -- several references make the same choice, presumably for the same reason.) Do you think it would help if I added row and column numbers along the outer border of the matrix? -- 899:, and Urve commented on it above. My view is that I'm using Harvard references in order to mention, in the text, the authors of particular works, along with pointers to those works. Some uses are unambiguously of this form (e.g., the first sentence of the section on juggling sequences). But I do agree that I'm maybe trying to have it both ways in some places, where I'm mentioning individual authors or papers and not 1289:.) Yes, this really fell off my radar as end-of-semester hecticness set in. Is it possible to get a revised sense of what issues you view as unaddressed / essential to be resolved? For example, I have marked some things as "done" above, but it is not clear to me if they are done to your satisfaction. (I realize there are still a number of cn tags in the article, as well.) Thanks very much, 613: 2017:) seem to mention it -- and the article on algebraic groups does not mention the associated Weyl group. Core partitions are probably a central object in dozens of research papers, parabolic subgroups in hundreds or more, so I think notability is not a concern. (Obviously I need to convince some friends to become Knowledge editors to fix these oversights.) About 42: 1554:

geometric flavor to the image so that you can see a pattern, but yeah. For reference, I studied math in undergrad, so it may be confusing for those even less mathematical training (though I suppose most readers of this article will have some). Perhaps an image that requires less explanation can be used, or the image might be omitted altogether as JBL suggested.

345: 1899:, and I have not found any serious issues with the article in my reading so far. I'm a physics person rather than a pure-math person, so I'm accustomed to technical prose without being too familiar with the details of this specific topic. Speaking from that background, I think it's a pretty nice page! Kudos to all those who have put serious work into it. 1026: 998: 959: 933: 813: 773: 723: 655: 2078:, it doesn't matter what type it is, but if you happen to be the kind of person who thinks about reflection groups then of course this is a crucial piece of identifying information. My first instinct is to remove both instances of "type A" from the section you mention, and to add a few words in the section 1984:, thanks for your comments! In the section on the representation theory, I could easily convert the Viennot reference to a (Viennot yyyy) reference by mild rewriting: "... introduced by Viennot in (Viennot yyyy)." That would reduce by 1 the number of distinct styles in the section. A worthwhile change? 1376:

Thanks again for all the work you've put into this. The current status is as follows: I have provided sources for factual claims as best I can; I've removed some material that ultimately I have not been able to adequately source. There are two cn tags still in the article. The rest of this comment

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The mention of multiple authors amused me, because really this is my individual work (of course with several improvements by other editors since it went live). Though it's not necessary to address the issue you raised, I thought I would take a swing at explaining. Mathematical journal writing often

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is a certain perspective on the study of geometry that focuses on collinearity (when points are on the same lines) and parallelism; the geometric transformations (like rotations, translations, reflections) that preserve these properties (so if several lines are parallel, they get transformed into new

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gives an etymology. I would write something shorter than the preceding if I write something.) On the other hand, I don't have any source for what I just wrote: it's a cobbled together synthesis from sources that don't mention the affine symmetric group at all, plus my personal understanding of how

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It seems even to me that at least one, maybe two, more grafs could be added summarizing the sections of the article past the definitions (Consider that the DYK hook fact mentioned the juggling connection ... this is something that should probably have been mentioned in the intro; some DYK reviewers,

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in like that (and then including it inconsistently thereafter) might be slightly puzzling. "What makes this lattice 'type A'? Do these things also have lattices of other types? What does the type tell me?" Maybe I'd say something like, "... forms a root lattice, specifically one of type A". Perhaps

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I also cannot reiterate strongly enough how personally I take your insinuation that I only cared about the existence of citations and not their quality. Assessing the quality of the sources here may have been beyond my depth, as I've said (and to put more crudely what I've said a few times already,

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has stepped back from reviewing; has David Eppstein taken over, or do we need to find a new reviewer? If the latter is the case, then the nomination should probably be set to request a second opinion, in the hopes that someone who can deal with the arcane mathematics text will be able to take over.

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ever singled this group out for particular attention in his work. Unfortunately searching that out will take more time than I have available in the near future. (It is possible that in some sense the history of this object studied for its own sake rather than as one example of an important family

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I will say, however, that it took me a bit to understand the image of the matrix since it uses dots for 1s and omitted zeros and lacks borders for individual rows and columns (if I understand it correctly, the lines delimit each group of three rows and columns). I know it's probably to give a more

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Yes, more historical information would be good. I note that I haven't written down anywhere that the combinatorial definition of the group was first given by Lusztig in 1986, for example. I am not sure whether it will be possible to source a full section's worth of historical content to reliable

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to GA rules caused by your inventing rules out of thin air, and (3) the damage to encyclopedia content creator goodwill caused by your turning what should be a much more straightforward evaluation process into a bureaucratic nightmare. Anyway, is there a reason why you haven't answered any of the

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understand from writing articles about court cases and legal topics the challenges of writing about an abstract subject, often seen as impenetrable by lay readers, where common usage within the field requires both the use of words used nowhere else in English discourse, and some words that take a

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It is possible that an editor who is trying to promote an article to GA-class (good article status) might add citations to basic facts such as "...the sky is blue...". This is a good thing, and the fact that the sky is not always blue does benefit from adding a citation. We can add citations for

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Failure to assume good faith like this is why I am not interested in finishing this review. "Multiple editors" did not try to intervene on Eppstein's behalf; in fact if there were any actions by multiple editors that might have served as effective intervention had they been more willing to take

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This looks better to me too. I might quibble that the rectangular rather than square aspect ratio of each matrix cell, and pixel graphics rather than vector graphics, are both suboptimal, but those are minor quibbles that shouldn't affect the discussion here, and they may be difficult to change

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As for his comments about "checking sourcing by whether there were lots of little blue numbered footnote markers and not by whether the material needed sources and whether the sources were adequate for the material", well, Dave, you need to get out of the math ghetto more. This is exactly the

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A lot of sentences in the definitions sections, and indeed throughout the article, use "one" in the third-person impersonal style. I do not know if this is standard in mathematics—if it is, and we use it in other math articles, and we're OK with doing that in math articles, and I can be shown

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citing those mentions to other authors or papers. I think I'd like to try to reach an agreement about which places current usage is acceptable (e.g., I feel strongly that this is the case for the section on juggling sequences) and which are not (I think Urve has a point that the section on

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At the very least it would provide a brief respite from the equations and diagrams, especially if there is the potential for it to be illustrated by the inevitable image of some dead old white guy, either painted in academic regalia or photographed in black and white staring intently at the

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I also was grateful for well-written prose, with few grammatical errors and no spelling errors. Nor were any facts repeated, or stated fragmentarily. I would like to think that this is coincident with having to write so precisely, and to a great extent in symbols, about such an abstract and

1774:, which seemed to me to be rigorous enough. Again, I think anyone looking for a review of an article that had been languishing at GAN unreviewed for six months should be grateful someone went and reviewed it at all rather than raising side-eyed comments about "the depth of the review". 267:

What about the third one: "The correspondence between the geometric and combinatorial representations for other elements is discussed below in § Connection between the geometric and combinatorial definitions.)"? This sentence has no substantive assertion beyond the structure of the

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and their corresponding descriptions; the first image's description there has a citation but I think that's more to support the "popular" claim. In this case (i.e. the article Affine symmetric group) the description is just kind of long and is in the article instead of under the

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Minor concerns: the manner in which it points to items in the literature is not perfectly uniform. I call this a "concern" rather than a "problem", because I don't think it impedes understanding, and life is too short for me to really care about the distinction between

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There are several ways of getting svg from pdf, but I'm not sure which of them if any play nicely with the LaTeX fonts. The workflow I use for that (opening in Adobe Illustrator and saving as svg) definitely doesn't work well with those fonts. Maybe someone else knows?

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And to complement a history section, I wonder if it might be possible to end briefly talking about the future. What's going on in research into affine symmetric groups? Are any interesting possibilities opening up? Any new questions to be answered? Maybe something like

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This is a nice suggestion but I think it would be impossible to source to secondary sources. (I could, like, go pull a bunch of conjectures and open problems from recent papers, but I think it would be impossible to justify any particular choices and avoid synth.)

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Hi Daniel Case, thanks very much for this review, both the positive feedback and constructive criticisms. I plan to respond in stages over the next several days. An initial version (with some bolded quotes of your comments and my interspersed responses) is below.

325:. This is a common occurrence in GANs I review; usually it stems from someone's efforts to expand the article prior to the nomination and accompanying failure to commensurately expand the intro. But here this is an exception, as it came out of wikiversity that way. 175:, but ... it does not look like we can let this slide any longer. I owe about four reviews, and the type of a person I am, I prefer to take the harder reviews that are always in the top bar (not least because some of my nominations have ended up there; in fact 1265:

Merry Christmas (two days late) and Happy New Year! Holiday greetings aside, I see that you have not been able to do any work on this article in a month. I know you're an academic and this is a busy time of year. Will you be able to resume after the holidays?

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For the second one, it's just explaining convention which is common (and necessary) in mathematical writing. Since convention is important and using different conventions can be seriously confusing, it may be better to leave it in the article rather than a

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The harm is not primarily to the article, but (1) to the Good Article process caused by your dragging out this review endlessly with demands for additional footnotes where no footnote is needed and where none of the GA rules justify such a demand, (2) the

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I think the juggling patterns illustration, given its long strip-like shape, would look better centered above the text, rather than off to the side sticking into the main text awkwardly, twice as wide as any other image. I did something sort of similar

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can point to, then leaving it as a redlink is the best thing (as it signals there's a new topic to develop). I like your instinct about the "type A" business. And if there's no obvious way to expand the "History" section, I think it's fine as is.

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There are a couple redlinks. This isn't a problem with the article itself, but if the content they should point to does exist somewhere, then they should be pipes or redirects. It's probably worth checking. No big deal if they stay as they are,

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So, I will do what I usually do ... print it out, do a light copy edit (to the extent possible for me here) and come back within a week's time with my thoughts based on the article's structure and non-math aspects. I will probably ask at

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Very short sections often read as unfinished to me. Here, "History" is only three sentences. It's serviceable, and I wouldn't object to a GA having a section like that, but I'd advise thinking a moment or two about whether it could be

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are a wonderful combinatorial gadget that I'm surprised no one has written anything about in Knowledge, but I have looked in all the obvious places and searched in various ways and I just don't think it's here. We have content about

341:, of "affine" so the reader has a chance to understand what it means in this context. Before I started reviewing the article I thought it might have been someone's name (some obscure French or French-speaking mathematician, perhaps? 1762:

I had thought my willingness to take on a GA review in this subject area, especially an article which I remind Dave had languished for months before anyone dared review it, might have been appreciated, and indeed it was, by

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This wouldn't be necessary to expand the intro, as it can be done with what's there already, but it might be nice to link from the intro, as soon as possible after the bolded statement of the subject in the lede (from which

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So far so good. I was wondering ... now that we've expanded the intro, is there any image in the article we could put in the intro as lede image? If not, is there one somewhere else? Can one be created relatively easily.

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A lot of sentences in the definitions sections, and indeed throughout the article, use "one" in the third-person impersonal style. ... is it possible to rewrite or recast those sentences such that we don't have to use

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For what it's worth at this point, I agree with JBL. The first CN tagged sentence is just describing the image of the matrix. It's not really making a claim that needs a citation. See for instance the images in

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is introduced; in the section on Lie algebras; and finally in the section on other affine Coxeter groups) where it is alluded to, but that's it. I can't decide how I feel about this: from the point of view of

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And that's it. I think these issues can reasonably be addressed within the usual week or so, and of course I can extend that time limit if it looks like you're making progress. So, I'm putting the article ...

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explicitly does not rule out this use. But it also suggests that such use should be limited only to situations where that is really the only way to do it, and I'm not sure we have that here. I also note that

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Representation theory and an affine Robinson–Schensted correspondence is pushing the boundary here, and maybe the section on Fully commutative elements and pattern avoidance as well) before I patch them. --

1285:, thanks for the ping and the holiday greetings -- the same to you! (I was up vaguely in your corner of the world for Thanksgiving -- took the wonderful Amtrak line along the Hudson, visiting family in 213:

for starting this review, and for your initial efforts! I will begin addressing some of the citation needed tags soon. However, there were three of them I wanted to discuss: the one at the top of

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Sure, it may take a while, but I'll get back here. Generally you're more than 50% done ... if I could suggest anything right now, it would be making sure everything that isn't currently cited is.

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to explicitly mention that type A is the one we're talking about. What do you think? Finally, about the short history section, if you search above on this page you'll see my comment there that

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I am glad to see that editors involved are already attending to the requested footnotes. And, since in the process of reviewing I looked at the original draft on Wikiversity and found the

299:, by People Who Know This Stuff, with advanced degrees, actual academic chairs and all, I will defer to that and consider the math substantially correct, beyond the need for any sort of 504:

we deprecated inline parenthetical refs a little over a year ago, there is no justification for doing things this way. Put them in tags and rewrite or recast the sentences. This is the

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review. I will say that, with the help of the various links, I was able to follow most of the article on a very minimal, conceptual level. The author(s) are to be commended for that.

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Thank you for your patience. I have completed a first run through at addressing or responding to your comments. I would be interested in your assessment of this progress. Thanks,

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I think reducing the number of distinct styles by 1 would be a slight but noticeable improvement, and since it's a quick fix, it's probably worthwhile. If there's nothing yet that

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I have edited the article too much to take over. The mathematics has all been reviewed; the only sticking point was that Case was demanding citations for sentences like the one in

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I have (temporarily) converted from the imperative to the third person, to be further resolved when I think about the rest of the "one can"s. So let's call this specific point

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Thank you! I have made those two changes (Viennot and type A). The wording of the new sentence in the section on other groups is a bit clunky, but I think it does the job. --

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in fact, insist that the hook fact be in the intro. I don't think that's always necessary and don't insist on it, but here I think it could and should easily have been done).

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I have added two short paragraphs to the introduction; together, I believe they mention the highlights of all major body sections of the article. I'm going to call this

2039: 1411:... since we're not in a better world, I'll recommend instead what I've done for years since someone at a DYK nom accepted OI but insisted I find some way to cite it: 1839:

GA nominations I've reviewed, I have queried the reliability of the sources. And I'm sure if I looked through other GA noms I've reviewed, I could find more examples.

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action (a reluctance I now fully understand) it was the many supportive emails I got from other participants in the math project about dealing with Diamond Dave here.

603:: What's going on in research into affine symmetric groups? Are any interesting possibilities opening up? Any new questions to be answered? Maybe something like that. 1226:

I did think about this a little when choosing the figure, and decided the risk of confusion was low. The figure DE linked is the one I would have chosen instead. --

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That's incredibly helpful, thanks. I was able to get into my office yesterday and pick up some books; I will put in a final push this week and ping again soon. --

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able to gather that it has some meaning that puts it, at least sometimes, in contrast to "infinite", but I would have liked a fuller understanding from the get-go.

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Ok so on one hand this point is obviously correct, and I would like to write a sentence (or maybe footnote) that explains it. (The ultimate explanation is that

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The only thing I'm a little worried about with this image is that symmetries of the tiling itself and symmetries of the colored tiling are not the same thing. —

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You are right about what MOS:MATH says, but wrong in this instance that it applies. That portion of the MOS is about definitions; for example, in the section

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OK ... I had meant to get this done over the weekend, but I couldn't, and then I had to work at the polls on Tuesday so that delayed this into the later week.

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It is a nice idea! I wish there were more people writing the kind of expository / state-of-the-field articles in mathematics that could be used for this. --

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PNG to produce images (same as for all the others I created in the article); if you know how to get SVG output from LaTeX, I'd be happy to hear about it! --

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I know how you feel, but I've been dinged myself for this sort of thing (uncited prefatory/introductory sentences) far too many times even though if I had

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What harm could it possibly do to the article? If you'd like to have someone else review it, I'd be happy to let it go and have them take a crack at it.

107: 1209:. I'm not sure it's really much of a problem. Anyone who would notice that it's an issue would also know to ignore the colors for sake of the example. — 1896: 99: 994:

I believe that Shi probably is notable. However, I'm not going to write an article about him in the near future, so I have removed the link.

2021:, I see that the classification of affine Coxeter groups is not clearly spelled out anywhere in the article -- there are a few spots (when 1950:

is introduced and used bothers me a bit. If a reader isn't familiar with the classification of root systems and related topics, dropping

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groups, and of course this concept is intimately related to the concept in Coxeter groups, but none of our articles on Coxeter groups (

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That said, I do think there are some other non-math issues besides the insufficient citations (Before I begin, let me just say that I

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To translate between the geometric and algebraic definitions, fix an alcove and consider the n hyperplanes that form its boundary

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Starting at "cycle type and reflection length", the article inexplicably begins using its Harvard references not only inline and

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To translate between the geometric and algebraic definitions, fix an alcove and consider the n hyperplanes that form its boundary

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So, honestly, I don't know why this was done here. But, and I must speak more boldly than I have otherwise in this review, it

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mathematicians use words. So I'm concerned about how to go about this in practice. Thoughts or suggestions are welcome. --

688:, and in the geometric construction of the affine symmetric group the elements are all affine transformations. The article 1206: 1661:

Hmm, I hadn't noticed that they're not perfect squares, thanks -- I've fiddled, now it's better. I am using LaTeX -: -->

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Well, the natural thing is the triangular tiling of the plane; I went and found one on commons with some color in it. --

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is legitimate. This is a matter of taste; perhaps the most serious thing I can say about it is that having effectively

1407:. Technically, you'd say you don't need any citation, and in a better world I'd agree with you, and that would be it. 1019:

I think the juggling patterns illustration, given its long strip-like shape, would look better centered above the text

896: 115: 17: 809:, for whatever reason -- I have merged related consecutive single-sentence paragraphs there into larger paragraphs. 559:" This to me is an implicit requirement that does not and should not need to be restated (even though, of course, it 168:

This article has sat unreviewed for six months now, likely because it's about an arcane (to most of us) math topic.

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is an affine permutation if and only if ". But the statement about permutation patterns is not a definition.

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I see about 15 uses of "one has", "one may", etc. -- some are clearly avoidable, I'll see what I can do with them.

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are deprecated. There's no problem with them in footnotes, like the former of the two variants you proposed above.

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and come in and kick everything over, over a relatively minor issue that you could have handled with much more

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it might be nice to link from the intro ... to some article, or perhaps the Wiktionary definition, of "affine"

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druthers, too, it wouldn't be necessary. Your proposed solution of moving cites up has always worked for me.

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endnotes. I think that would work here, and then the remaining sentence could be joined into the next graf.

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As for the second one, I think, I typically put such meta references of the "In this article ..." type into

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but it did not work well so I self-reverted. May try again later (1st day of classes is tomorrow) .... --

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In other words, is it possible to rewrite or recast those sentences such that we don't have to use "one"?

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Do not close a review started by another reviewer without first attempting to contact the first reviewer

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So you would have more respect for me if I had lied? I'll keep that in mind next time. If there is one.

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Might those parentheticals at the end of a couple of grafs be better off converted into endnotes using

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And to complement a history section, I wonder if it might be possible to end briefly talking about the

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If J.Y. Shi's notability can be demonstrated, start at least a stub article. Otherwise delink his name.

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Might those parentheticals at the end of a couple of grafs be better off converted into endnotes using

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for someone not involved with the article to take a look at the math and let me know how solid it is.

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criterion by which GANs in every other subject area are reviewed. I commend to your reading attention

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Yes I think adding row/column numbers may help, and would also allow the description to be shortened.

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require a consistent citation style throughout the article, but ... I would commend your attention to

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things that are well-known, and the source can contain additional information to benefit our readers.

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is an affine permutation if ." The admonition in MOS is that I should not have written "a function

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rather than even the most feeble denial? (Also, please do not call me "Dave"; it is not my name.) —

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be undone to be consistent with the citations in the first half of the article. I see nothing in

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Why would I apologize, when your response to my accusation of superficial reference-checking is

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we should try to combine them with adjacent, longer grafs, unless there is a good reason not to.

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First, at 60K total, it is long enough that the intro can and should be more than the one graf.

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Hey, we should all try to stretch ourselves and push the limit on what we think we can do ...

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examples, I drop any perceived objections. However, I have seen it nowhere else on Knowledge.

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to mention, in the text, the authors of particular works, along with pointers to those works

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One thing that might help make for a longer intro is something many of our other conceptual

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Those changes look good to me. I'm inclined to say the article deserves GA status now. The

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My opinion of this hasn't really changed since then. Thanks again for your comments! --

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Oops, I could have sworn I responded here yesterday, but it seems I never hit "publish".

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As in so many other sciences, a lot of people leave their mark on the field that way) I

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the text or the figure caption could mention that the triangular lattice is known as A

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for now. I believe it would be possible to write a more detailed history section on

414:. That's common in a textbook, but we generally try to avoid that in an encyclopedia. 334: 270:

Never mind, I see, it's a two-sentence parenthetical. Back to the bookshelf .... --

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strongly suggests that the use of pronouns to address the reader should be avoided.

2156:, but in this case the first reviewer appears to have distanced from the article. 1324:

Alright. Looking everything over, I think all that's left is the six places where

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Now let me move towards addressing the point. There was a discussion about this

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To make such a remark so recklessly warrants an apology, but I'm not hopeful.

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I believe it would be possible to write a more detailed history section on

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be undone. We can't have two different cite styles within the same article.

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There are also a fair amount of free-standing single-sentence grafs. Per

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Because I'm done with this review right here and right now, that's why.

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Yes, nice suggestion, and thank you for showing me how it can be done.

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of articles that seem like they would provide the necessary explanation

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It's easier to find a citation than to argue over why it is not needed

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complicated subject. If so, it speaks well of mathematics as a field.

1937:

Representation theory and an affine Robinson–Schensted correspondence

452:. Going back to the above link to MOS:MATH, it explicitly says that " 360: 1821: 1808:

been willing to meet me halfway on this, and I was really just that

837:. Going back to the above link to MOSMATH, it explicitly says that " 802:

There are also a fair amount of free-standing single-sentence grafs.

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citations within any given article should follow a consistent style.

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I didn't myself feel anywhere near qualified to choose the best one.

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Affine_symmetric_group#Combinatorics_of_other_affine_Coxeter_groups

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suggesting that citations can be used this way, and given that per

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nonstandard meaning that cannot be easily intuited from context):

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Affine symmetric group#Relationship to the finite symmetric group

1935:— is too choppy. This particularly sticks out in the subsection 719:

I have significantly reduced the number of these; let's call it

2088:, but I am skeptical that there is a lot more to be said about 784:, but I am skeptical that there is a lot more to be said about 1770:

Yes, I'm not a higher level mathematician, so I relied on the

1911:. I see that this has been discussed above, and I think that 839:

When defining a term, do not use the phrase 'if and only if'.

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When defining a term, do not use the phrase 'if and only if'.

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issue away from ending the review with a promotion when you

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critiques of the math sourcing in the WikiJournal of Science

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tags remain. Fix those and we're pretty much (ahem) good.

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a link that could be made, from the third sentence; while

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A 2019 paper by Lewis et al. proved the following formula

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In (Lewis et al. 2019), the following formula was proved

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Affine symmetric group#Descents, length, and inversions

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Oh ... OK ... I see what you're saying and I hear you.

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been monitoring this and I'm OK with your decision.

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It 2070: 2033: 1205:Only by using a much less eye-catching image like 769:I have made a first attempt at this, so let's say 323:the intro can and should be more than the one graf 512:after getting all the material properly sourced. 684:lines that are still parallel, etc.) are called 1786: 1640:depending on how you're generating the image. — 846:Affine symmetric group#Combinatorial definition 456:" Some of the other guidance there is on point. 419:math articles that have gained at least GA have 223:Affine symmetric group#Combinatorial definition 805:This was particularly the case in the section 988:expertise for their opinion on this question. 8: 1400:These cats can be skinned in different ways. 1191:Is this something that can be easily fixed? 833:I actually seemed to have been right before 448:I actually seemed to have been right before 321:First, at 60K total, it is long enough that 1828:tact at all would have been an improvement. 749:sources; for example, I don't know whether 711:Ha, gosh, and I was so proud of myself for 649:Yes, absolutely I agree, I will work on it. 30: 2062: 2051: 2050: 2047: 2026: 2090:the affine symmetric group in particular 1722:(Or perhaps a request should be made at 786:the affine symmetric group in particular 335:we are strongly discouraged from linking 955:This is a chronic flaw in my writing. 848:, the second sentence says "a function 61: 33: 2153: 2083: 1951: 1947: 1936: 1932: 1928: 1924: 1916: 1908: 1904: 1858: 1414:See accompanying diagram</ref: --> 1403:For the first one, you're leaning on 990:So based on David Eppstein's comment 7: 2071:{\displaystyle {\widetilde {S}}_{n}} 342: 1496:questions in my previous comment? — 952:? They sort of read that way to me. 438:? They sort of read that way to me. 2028: 1451:can you please re-read the actual 754:only dates back < 40 years.) -- 215:Affine symmetric group#Definitions 24: 1946:Something about the way the term 2086:affine Coxeter groups in general 1923:citation styles — a footnote to 1024: 996: 984:I am querying someone with more 957: 931: 811: 782:affine Coxeter groups in general 771: 721: 653: 611: 343: 265:Great, thanks, I will do that. 2195:Thank you for letting me know! 1832:beggars can't be choosers). In 1767:who was working on the article. 337:), to some article, or perhaps 1: 2205:21:00, 17 February 2022 (UTC) 2191:20:49, 17 February 2022 (UTC) 2166:20:32, 17 February 2022 (UTC) 2144:12:28, 17 February 2022 (UTC) 2123:02:26, 17 February 2022 (UTC) 2104:01:02, 17 February 2022 (UTC) 1976:20:54, 16 February 2022 (UTC) 1885:19:19, 16 February 2022 (UTC) 1871:16:07, 16 February 2022 (UTC) 1852:08:28, 16 February 2022 (UTC) 1755:06:54, 16 February 2022 (UTC) 1736:05:42, 16 February 2022 (UTC) 1313:05:39, 31 December 2021 (UTC) 1299:00:44, 29 December 2021 (UTC) 1276:01:04, 28 December 2021 (UTC) 1207:File:Uniform tiling 63-t2.svg 1180:08:21, 30 November 2021 (UTC) 1166:06:35, 30 November 2021 (UTC) 1148:00:23, 28 November 2021 (UTC) 1127:07:05, 18 November 2021 (UTC) 1104:12:25, 16 November 2021 (UTC) 1078:12:25, 16 November 2021 (UTC) 1064:22:56, 15 November 2021 (UTC) 1015:14:49, 15 November 2021 (UTC) 914:12:25, 16 November 2021 (UTC) 798:14:49, 15 November 2021 (UTC) 764:11:48, 10 November 2021 (UTC) 740:11:48, 10 November 2021 (UTC) 703:11:48, 10 November 2021 (UTC) 1688:01:53, 16 January 2022 (UTC) 1673:01:49, 16 January 2022 (UTC) 1650:02:09, 14 January 2022 (UTC) 1635:02:05, 14 January 2022 (UTC) 1614:02:35, 11 January 2022 (UTC) 1600:21:15, 10 January 2022 (UTC) 1582:21:12, 10 January 2022 (UTC) 1564:10:43, 10 January 2022 (UTC) 1535:05:59, 10 January 2022 (UTC) 1506:05:40, 10 January 2022 (UTC) 1486:05:37, 10 January 2022 (UTC) 1465:05:32, 10 January 2022 (UTC) 1439:04:59, 10 January 2022 (UTC) 1236:15:35, 3 December 2021 (UTC) 1219:07:12, 2 December 2021 (UTC) 1201:06:04, 2 December 2021 (UTC) 1042:12:17, 9 November 2021 (UTC) 976:12:17, 9 November 2021 (UTC) 880:18:50, 5 November 2021 (UTC) 870:OK, no problem ... I defer. 866:12:17, 9 November 2021 (UTC) 829:12:17, 9 November 2021 (UTC) 672:12:17, 9 November 2021 (UTC) 631:06:14, 4 November 2021 (UTC) 577:19:06, 5 November 2021 (UTC) 539:You are correct in that the 529:09:06, 4 November 2021 (UTC) 470:05:47, 4 November 2021 (UTC) 382:05:15, 4 November 2021 (UTC) 280:23:44, 28 October 2021 (UTC) 261:18:25, 28 October 2021 (UTC) 235:18:01, 28 October 2021 (UTC) 221:, and the one at the end of 200:03:49, 26 October 2021 (UTC) 161:03:49, 26 October 2021 (UTC) 1387:00:57, 7 January 2022 (UTC) 1365:01:53, 5 January 2022 (UTC) 1344:22:54, 4 January 2022 (UTC) 1152:Looks good ... we got some 18:Talk:Affine symmetric group 2233: 1054:OK; it was just an idea. 565:featured article criteria 339:the Wiktionary definition 2034:{\displaystyle \Lambda } 897:on the article talk-page 533:Harvard references used 217:, the one at the top of 1625:Indeed! It is done. -- 205:Comments from JayBeeEll 171:I am not a math person 2072: 2035: 1791: 686:affine transformations 361:we do have at least a 2073: 2036: 1453:good article criteria 690:Affine transformation 541:good article criteria 2046: 2025: 1156:action going there! 918:And per the above, " 406:And per the above, " 179:is there as I type. 2019:type A root lattice 1991:parabolic subgroups 1948:type A root lattice 1254:Christmas greetings 835:this partial revert 450:this partial revert 2068: 2031: 1818:the angry mastodon 1794:And there is also 1765:every other editor 888:Harvard references 479:sentences, but as 297:peer reviews there 2059: 1225: 460:Saving again ... 209:Thanks very much 89: 88: 2224: 2176: 2133: 2077: 2075: 2074: 2069: 2067: 2066: 2061: 2060: 2052: 2040: 2038: 2037: 2032: 2007:Reflection group 1931:and also inline 1796:this section hed 1660: 1624: 1475: 1450: 1428: 1422: 1415: 1397: 1375: 1354: 1333: 1327: 1323: 1264: 1223: 1190: 1137: 1115: 1093: 1032: 1028: 1027: 1004: 1000: 999: 965: 961: 960: 951: 945: 939: 935: 934: 819: 815: 814: 779: 775: 774: 729: 725: 724: 661: 657: 656: 615: 437: 431: 355:As it is, there 348: 347: 346: 246: 139: 130: 111: 43:Copyvio detector 31: 2232: 2231: 2227: 2226: 2225: 2223: 2222: 2221: 2170: 2127: 2049: 2044: 2043: 2023: 2022: 2015:Coxeter diagram 1986:Core partitions 1958: 1708: 1654: 1618: 1469: 1444: 1426: 1420: 1412: 1391: 1369: 1348: 1331: 1325: 1317: 1287:Columbia County 1258: 1256: 1184: 1131: 1109: 1087: 1025: 1023: 997: 995: 958: 956: 949: 943: 932: 930: 812: 810: 772: 770: 744:history section 722: 720: 681:affine geometry 654: 652: 638: 621:Happy editing! 435: 429: 344: 290: 240: 207: 120: 97: 91: 85: 57: 29: 22: 21: 20: 12: 11: 5: 2230: 2228: 2220: 2219: 2218: 2217: 2216: 2215: 2214: 2213: 2212: 2211: 2210: 2209: 2208: 2207: 2110:core partition 2065: 2058: 2055: 2030: 2011:Dynkin diagram 1964: 1960: 1956: 1944: 1940: 1900: 1893: 1892: 1891: 1890: 1889: 1888: 1887: 1863:David Eppstein 1792: 1784: 1747:David Eppstein 1726:?) Thank you. 1715:David Eppstein 1707: 1704: 1703: 1702: 1701: 1700: 1699: 1698: 1697: 1696: 1695: 1694: 1693: 1692: 1691: 1690: 1680:David Eppstein 1657:David Eppstein 1642:David Eppstein 1602: 1551: 1547: 1523: 1522: 1521: 1520: 1519: 1518: 1517: 1516: 1515: 1514: 1513: 1512: 1511: 1510: 1509: 1508: 1498:David Eppstein 1472:David Eppstein 1457:David Eppstein 1367: 1255: 1252: 1251: 1250: 1249: 1248: 1247: 1246: 1245: 1244: 1243: 1242: 1241: 1240: 1239: 1238: 1211:David Eppstein 1187:David Eppstein 1172:David Eppstein 1085: 1084: 1083: 1082: 1081: 1080: 1048: 1044: 1020: 1017: 981: 978: 953: 940: 927: 916: 893: 889: 885: 884: 883: 882: 842: 831: 803: 800: 767: 745: 742: 709: 705: 677: 674: 646: 637: 634: 605: 604: 597: 589: 585: 584: 583: 582: 581: 580: 508:thing in this 506:most essential 458: 457: 446: 439: 426: 415: 404: 370: 369: 330: 289: 286: 285: 284: 283: 282: 206: 203: 140: 87: 86: 84: 83: 78: 73: 67: 64: 63: 59: 58: 56: 55: 53:External links 50: 45: 39: 36: 35: 28: 25: 23: 15: 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